Three-magnon splitting and confluence processes for spin-wave excitations in yttrium iron garnet films: Wave vector selective Brillouin light scattering measurements and analysis

Brillouin light scattering (BLS) has been used to observe and confirm the existence of nonlinear three magnon splitting and confluence processes for propagating spin waves in the magnetostatic backward volume wave configuration. Wave vector and frequency selective BLS techniques were also used to provide a quantitative map of the wave vector make-up for the parametrically excited half-frequency dipole-exchange spin wave (DESW) split magnons and the confluence magnons that result from the recombination of these DESW modes. The experimental wave vector maps for the product splitting and confluence magnons matched nicely with those expected from spin-wave theory. The data were obtained with (1) a strip line excitation/detection transducer structure, (2) forward-scattering BLS optics, (3) a fixed magnetic field of 352 Oe applied along the propagation direction, (4) pumping frequencies from 2.5 down to 2.1 GHz, (5) and cw input powers from $200\mu \text{W}$ to 6 mW. The wave vector selective measurements utilized variable diameter circular diaphragms, rotatable slit apertures, and circular light blocks to access spin waves with wave numbers from about 100 to $3.6\times {10}^4\text{rad}/\text{cm}$ and the full $360°$ range of propagation angles.

Figure 1

Schematic diagram of the wave vector selection scattering geometry. The laser light is incident on the yttrium iron garnet film spin-wave propagation structure at wave vector ${\mathbf{q}}_i$, with a scattered light wave vector ${\mathbf{q}}_s$ and a magnon wave vector ${\mathbf{k}}_{\text{max}}$ oriented at an angle ${\theta }_{\text{max}}$ relative to the direction of the applied field $\mathbf{H}$. The collection lens and the diaphragm slit assembly define the selected magnon wave vector.

Figure 2

Representative Brillouin light scattering spectra of scattering intensity vs frequency for different input microwave cw power levels $\left(P_{\text{in}}\right)$, as indicated. The pump frequency $\left(f_p\right)$ was 2.5 GHz. The static external field was set to 352 Oe. The nominal spectrometer free spectral range was 8 GHz. There were no wave vector selective diaphragms in place and the measuring time was the same for all scans. The vertical dashed lines and labels identify different peaks in the spectra at $f_p$, at $f_c$, slightly below $f_p$, and at $f_p/2$.

Figure 3

Schematic dispersion curves of spin-wave frequency $f_k$ vs wave number $k$ with mode connections. The curves are for the first six dipole-exchange spin-wave branches for in-plane propagation parallel or antiparallel to the field $H$ and an $H$ value of 352 Oe, the same as for the data in Fig. 2. The horizontal dashed lines label the frequencies for the three peaks identified in Fig. 2 for the directly pumped magnetostatic backward volume wave spin waves at $f_p=2.5\text{GHz}$, confluence magnons at $f_c$, and splitting magnons at $f_p/2$. The open diamond at $f_p$ labels the MSBVW operating point. The matching pairs of solid and open circles and squares show, in schematic form, parametrically excited split magnons at $\pm k$ and with $f_k$ values equally shifted up and down from the $f_p/2$ line. The open diamonds for a range of low $\left|k\right|$ values on the $f_c$ line show the nominal position in frequency and wave number for the confluence magnons. The dashed square close to 1.12 GHz identifies split magnons that give a confluence magnon at $f_c$.

Figure 4

(a) BLS scattering signal at $f_p/2$ as a function of the maximum allowed wave number $k_{\text{max}}$ for an input power of 5.56 mW and $f_p=2.5\text{GHz}$. The vertical dashed lines denote the limit $k_{\text{max}}$ values for the experimental diaphragm setup. (b) Theoretical isofrequency contour plots of the transverse in-plane spin-wave wave vector component $k_{\perp }$ vs the parallel component $k_{\parallel }$ for the three lowest-order DESW modes at $f_p/2$. The plot was obtained from the DESW theory of Ref. 16, with parameters that match the experiment. The open circles and $k_0$ labels mark the low limit for the available DESW spin waves at $f_p/2$. The angle ${\theta }_{k-s}^{\text{max}}$ labeled in (b) shows the maximum allowed spin-wave propagation angle.

Figure 5

Polar representation of the BLS signal for the $f_p/2$ DESW magnon peak as a function of the slit aperture rotation angle ${\theta }_k$. The arrow shows the direction of the static field $H$. The dashed lines denote the double sector of spin-wave propagation angles for $-{\theta }_{k-s}^{\text{max}}<{\theta }_k<{\theta }_{k-s}^{\text{max}}$ and $\left(180°-{\theta }_{k-s}^{\text{max}}\right)<{\theta }_k<\left(180°+{\theta }_{k-s}^{\text{max}}\right)$ that match the range of allowed ${\theta }_k$ values from Fig. 4b.

Figure 6

(a) Data on the BLS scattering signal level at the $f_c$ peak vs the two limit wave numbers $k_{\text{min}}$ and $k_{\text{max}}$, as obtained for different diameter light blocks or diaphragms, respectively. The dashed light gray area gives a qualitative estimate of the confluence magnon $k$ distribution implied by these data. (b) Theoretical isofrequency contour plots of the transverse in-plane spin-wave wave vector component $k_{\perp }$ vs the parallel component $k_{\parallel }$, as referenced to the field direction, for the three lowest-order DESW modes at $f_c$. The plot was obtained from the DESW theory of Ref. 16, with parameters that match the experiment. The angle ${\theta }_{k-c}^{\text{max}}$ corresponds to the maximum allowed spin-wave propagation angle for confluence magnons at the $f_c$ frequency cut. (c) Polar representation of the BLS signal level at the $f_c$ peak as a function of the slit aperture rotation angle for the input power of 5.56 mW. The arrow shows the direction of the static magnetic bias field $\mathbf{H}$.

Figure 7

Representative BLS spectra of scattering intensity vs frequency for different pumping frequencies. (a) $f_p=2.4\text{GHz}$, (b) $f_p=2.3\text{GHz}$, (c) $f_p=2.2\text{GHz}$, and (d) $f_p=2.1\text{GHz}$. The static external field was set to 352 Oe. The nominal spectrometer free spectral range was 8 GHz. There were no wave vector selective diaphragms or light blocks in place and the measuring time was the same for all scans. The vertical dashed lines and labels identify different peaks in the spectra at $f_p$, at $f_c$, and at $f_p/2$.